Download or read book Cabal Seminar 77 79 written by A. S. Kechris and published by Springer. This book was released on 2006-11-15 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cabal Seminar 76 77 written by A. S. Kechris and published by Springer. This book was released on 2006-11-15 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cabal Seminar 76 77 written by and published by . This book was released on 1978 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Course on Borel Sets written by S.M. Srivastava and published by Springer. This book was released on 2013-12-01 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The roots of Borel sets go back to the work of Baire [8]. He was trying to come to grips with the abstract notion of a function introduced by Dirich let and Riemann. According to them, a function was to be an arbitrary correspondence between objects without giving any method or procedure by which the correspondence could be established. Since all the specific functions that one studied were determined by simple analytic expressions, Baire delineated those functions that can be constructed starting from con tinuous functions and iterating the operation 0/ pointwise limit on a se quence 0/ functions. These functions are now known as Baire functions. Lebesgue [65] and Borel [19] continued this work. In [19], Borel sets were defined for the first time. In his paper, Lebesgue made a systematic study of Baire functions and introduced many tools and techniques that are used even today. Among other results, he showed that Borel functions coincide with Baire functions. The study of Borel sets got an impetus from an error in Lebesgue's paper, which was spotted by Souslin. Lebesgue was trying to prove the following: Suppose / : )R2 -- R is a Baire function such that for every x, the equation /(x,y) = 0 has a. unique solution. Then y as a function 0/ x defined by the above equation is Baire.
Download or read book Handbook of Set Theory written by Matthew Foreman and published by Springer Science & Business Media. This book was released on 2009-12-10 with total page 2200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.
Download or read book Sets and Extensions in the Twentieth Century written by and published by Elsevier. This book was released on 2012-01-24 with total page 878 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration Serves as a singular contribution to the intellectual history of the 20th century Contains the latest scholarly discoveries and interpretative insights
Download or read book Extensions of the Axiom of Determinacy written by Paul B. Larson and published by American Mathematical Society. This book was released on 2023-10-19 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an expository account of work on strong forms of the Axiom of Determinacy (AD) by a group of set theorists in Southern California, in particular by W. Hugh Woodin. The first half of the book reviews necessary background material, including the Moschovakis Coding Lemma, the existence of strong partition cardinals, and the analysis of pointclasses in models of determinacy. The second half of the book introduces Woodin's axiom system $mathrm{AD}^{+}$ and presents his initial analysis of these axioms. These results include the consistency of $mathrm{AD}^{+}$ from the consistency of AD, and its local character and initial motivation. Proofs are given of fundamental results by Woodin, Martin, and Becker on the relationships among AD, $mathrm{AD}^{+}$, the Axiom of Real Determinacy, and the Suslin property. Many of these results are proved in print here for the first time. The book briefly discusses later work and fundamental questions which remain open. The study of models of $mathrm{AD}^{+}$ is an active area of contemporary research in set theory. The presentation is aimed at readers with a background in basic set theory, including forcing and ultrapowers. Some familiarity with classical results on regularity properties for sets of reals under AD is also expected.
Download or read book Logic Colloquium 2006 written by S. Barry Cooper and published by Cambridge University Press. This book was released on 2009 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume, with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. The most topical areas of current research are covered: valued fields, Hrushovski constructions (from model theory), algorithmic randomness, relative computability (from computability theory), strong forcing axioms and cardinal arithmetic, large cardinals and determinacy (from set theory), as well as foundational topics such as algebraic set theory, reverse mathematics, and unprovability. This volume will be invaluable for experts as well as those interested in an overview of central contemporary themes in mathematical logic.
Download or read book Stochastic Integrals written by D. Williams and published by Springer. This book was released on 2006-11-15 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Set Theory of the Continuum written by Haim Judah and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Primarily consisting of talks presented at a workshop at the MSRI during its "Logic Year" 1989-90, this volume is intended to reflect the whole spectrum of activities in set theory. The first section of the book comprises the invited papers surveying the state of the art in a wide range of topics of set-theoretic research. The second section includes research papers on various aspects of set theory and its relation to algebra and topology. Contributors include: J.Bagaria, T. Bartoszynski, H. Becker, P. Dehornoy, Q. Feng, M. Foreman, M. Gitik, L. Harrington, S. Jackson, H. Judah, W. Just, A.S. Kechris, A. Louveau, S. MacLane, M. Magidor, A.R.D. Mathias, G. Melles, W.J. Mitchell, S. Shelah, R.A. Shore, R.I. Soare, L.J. Stanley, B. Velikovic, H. Woodin.
Download or read book Recursion Theory written by Anil Nerode and published by American Mathematical Soc.. This book was released on 1985 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Axiomatic Set Theory written by James E. Baumgartner and published by . This book was released on 1984 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ordinal Definability and Recursion Theory Volume 3 written by Alexander S. Kechris and published by Cambridge University Press. This book was released on 2016-01-11 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Ordinal Definability and Recursion Theory is the third in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'HOD and its Local Versions' (Part V) and 'Recursion Theory' (Part VI), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist.
Download or read book Advances in Mathematical Logic written by Toshiyasu Arai and published by Springer Nature. This book was released on 2022-01-24 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gaisi Takeuti was one of the most brilliant, genius, and influential logicians of the 20th century. He was a long-time professor and professor emeritus of mathematics at the University of Illinois at Urbana-Champaign, USA, before he passed away on May 10, 2017, at the age of 91. Takeuti was one of the founders of Proof Theory, a branch of mathematical logic that originated from Hilbert's program about the consistency of mathematics. Based on Gentzen's pioneering works of proof theory in the 1930s, he proposed a conjecture in 1953 concerning the essential nature of formal proofs of higher-order logic now known as Takeuti's fundamental conjecture and of which he gave a partial positive solution. His arguments on the conjecture and proof theory in general have had great influence on the later developments of mathematical logic, philosophy of mathematics, and applications of mathematical logic to theoretical computer science. Takeuti's work ranged over the whole spectrum of mathematical logic, including set theory, computability theory, Boolean valued analysis, fuzzy logic, bounded arithmetic, and theoretical computer science. He wrote many monographs and textbooks both in English and in Japanese, and his monumental monograph Proof Theory, published in 1975, has long been a standard reference of proof theory. He had a wide range of interests covering virtually all areas of mathematics and extending to physics. His publications include many Japanese books for students and general readers about mathematical logic, mathematics in general, and connections between mathematics and physics, as well as many essays for Japanese science magazines. This volume is a collection of papers based on the Symposium on Advances in Mathematical Logic 2018. The symposium was held September 18–20, 2018, at Kobe University, Japan, and was dedicated to the memory of Professor Gaisi Takeuti.
Download or read book Fundamentals of Stability Theory written by John T. Baldwin and published by Cambridge University Press. This book was released on 2017-03-02 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the twelfth publication in the Perspectives in Logic series, John T. Baldwin presents an introduction to first order stability theory, organized around the spectrum problem: calculate the number of models a first order theory T has in each uncountable cardinal. The author first lays the groundwork and then moves on to three sections: independence, dependence and prime models, and local dimension theory. The final section returns to the spectrum problem, presenting complete proofs of the Vaught conjecture for ω-stable theories for the first time in book form. The book provides much-needed examples, and emphasizes the connections between abstract stability theory and module theory.
Download or read book Books in Print written by and published by Reed Reference Publishing. This book was released on 1993-09 with total page 1740 pages. Available in PDF, EPUB and Kindle. Book excerpt: V. 1. Authors (A-D) -- v. 2. Authors (E-K) -- v. 3. Authors (L-R) -- v. 4. (S-Z) -- v. 5. Titles (A-D) -- v. 6. Titles (E-K) -- v. 7. Titles (L-Q) -- v. 8. Titles (R-Z) -- v. 9. Out of print, out of stock indefinitely -- v. 10. -- Publishers.
Download or read book Numerical Analysis written by G.A. Watson and published by Lecture Notes in Mathematics. This book was released on 1980-02 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
